Using the rule of 78s,a borrower who repaid a 12-month loan after only 5 months would save ____ of his or her interest.

Question

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The rule of 78s is a method used in lending that pre-calculates the total interest over the life of a loan and assigns a larger portion of interest to the early payments. If a borrower repays a 12-month loan after only 5 months, they would save the interest assigned to the remaining 7 months. According to the rule of 78s, the sum of the digits from 1 to 12 (1+2+3+...+12) equals 78. The interest for the remaining 7 months is calculated as the sum of the digits from 6 to 12 (6+7+8+9+10+11+12 = 63). However, the question asks for the saved interest after 5 months, which corresponds to the interest assigned to the first 5 months, calculated as the sum of the digits from 1 to 5 (1+2+3+4+5 = 15). Therefore, the saved interest is represented by 15 out of the total 78, which simplifies to 15/78. However, the provided options do not directly match this calculation, suggesting a misunderstanding in the explanation or a mistake in the calculation based on the provided options. The correct interpretation, based on the options given, would be to understand how much interest is saved compared to the total interest calculated by the rule of 78s, which is not directly represented by the sum of the first 5 months but rather the concept of how the rule of 78s distributes interest savings when a loan is paid off early. The correct answer, based on the options and understanding of the rule of 78s, should reflect the proportion of interest saved by not having to pay the interest assigned to the later months of the loan term.

Using the Rule of 78s,a Borrower Who Repaid a 12-Month